化学锚栓计算:采用四个5.6级斯泰NG-M12×110粘接型(化学)锚栓后锚固,h ef=110mm,A S=58mm2,f u=500N/mm2 ,f y=300N/mm2。
荷载大小:N=5.544 KNV=2.074 KNM=2.074×0.08=0.166 KN·m一、锚栓内力分析1、受力最大锚栓的拉力设计值因为361221 5.544100.166105042250My N n y ⨯⨯⨯-=-⨯⨯∑=556 N >0 故,群锚中受力最大锚栓的拉力设计值:12i h Sd My NN n y =+∑ 3625.544100.166105042250⨯⨯⨯=+⨯⨯ =2216 N2、承受剪力最大锚栓的剪力设计值化学锚栓有效锚固深度:ef h '=ef h -30=60 mm锚栓与混凝土基材边缘的距离c=150 mm <10ef h '=10×60=600 mm ,因此四个锚栓中只有部分锚栓承受剪切荷载。
承受剪力最大锚栓的剪力设计值:2hSd VV ==2074/2=1037 N 二、锚固承载力计算 1、锚栓钢材受拉破坏承载力锚栓钢材受拉破坏承载力标准值: ,5850029000Rk s s stk N A f ==⨯=N 锚栓钢材破坏受拉承载力分项系数:锚栓钢材破坏时受拉承载力设计值:,,,29000145002.0Rk sRd s RS NN N γ===N >h SdN=2216 N锚栓钢材受拉承载力满足规范要求! 2、混凝土锥体受拉破坏承载力 锚固区基材为开裂混凝土。
单根锚栓理想混凝土锥体破坏时的受拉承载力标准值:=8248.64 N混凝土锥体破坏情况下,确保每根锚栓受拉承载力标准值的临界间距: ,33(9030)180mm cr Nef s h '==⨯-=混凝土锥体破坏情况下,确保每根锚栓受拉承载力标准值的临界边距: , 1.5 1.5(9030)90mm cr N ef c h '==⨯-= 基材混凝土劈裂破坏的临界边距:,22(9030)120mm cr spef ch '==⨯-=则,c 1=150 mm >,90cr N c =mm ,取c 1=90 mm 边距c 对受拉承载力降低影响系数:,,900.70.30.70.390s N cr Nc c ψ=+=+⨯=1.0表层混凝土因密集配筋的剥离作用对受拉承载力降低影响系数:,90300.50.5200200efre Nh ψ-=+=+=0.8荷载偏心对受拉承载力的降低影响系数:,,111.012/120ec N N cr Ne s ψ===++⨯其中,0Ne =开裂混凝土, 1.0ucr N ψ=单根锚栓受拉,混凝土理想化破坏锥体投影面面积:0222,,18032400mm c N cr NA s ===s 1=100 mm <,取,180cr N s mm =s 1=100 mms 2=200 mm >,180cr Ns mm =,取s 2=180 mmc 1=150 mm >,90mm cr N c =,取c 1=90 mm ,c 2=90 mm群锚受拉,混凝土破坏锥体投影面面积,c N A :,11,22,(c 0.5)(0.5)c N cr N cr N A s s c s s =++++(901000.5180)(901800.5180)=++⨯++⨯=100800 mm 2混凝土锥体破坏时的受拉承载力分项系数,, 2.15Rc N γ=群锚混凝土锥体受拉破坏时的受拉承载力标准值:,0,,,,,,0,c N Rk c Rk cs N re N ec N ucr N c NA N NAψψψψ=1008008248.64 1.00.8 1.0 1.032400=⨯⨯⨯⨯⨯=20529.95 N群锚混凝土锥体受拉破坏时的受拉承载力设计值:,,,20529.959548.812.15Rk cRd c Rc NN N γ===N >N=5544 N混凝土锥体受拉承载力满足规范要求! 3、混凝土劈裂破坏承载力基材混凝土劈裂破坏的临界边距:,22(9030)120mm cr spef ch '==⨯-=则,c 1=150 mm >,120mm cr sp c =,取c 1=120 mm ,c 2=120 mm,,22120240mm cr sp cr sp s c ==⨯=s 1=100 mm <,240cr sp s mm =,取s 1=100 mms 2=200 mm >,240cr spsmm =,取s 2=200 mm0222,,24057600mm c N cr spA s === ,11,22,(c 0.5)(0.5)c N cr sp cr sp A s s c s s =++++(1201000.5240)(1202000.5240)=++⨯⨯++⨯=149600 mm 2构件厚度h 对劈裂承载力的影响系数:2233h,250()()2260spef h h ψ==⨯=1.631>1.5,取h, 1.5sp ψ=单根锚栓理想混凝土锥体破坏时的受拉承载力标准值:,0 3.0(30)Rk c efN h =-1.53.0(9030)=⨯- =8248.64 N群锚混凝土锥体受拉破坏时的受拉承载力标准值:,0,,,,,,0,c N Rk c Rk cs N re N ec N ucr N c NA N NAψψψψ=1496008248.64 1.00.8 1.0 1.057600=⨯⨯⨯⨯⨯=17138.84 N混凝土劈裂破坏受拉承载力标准值:,,, 1.517138.8425708.26Rk sp h sp Rk c N N ψ==⨯=N混凝土劈裂破坏受拉承载力设计值:,,/25708.26/2.1511957.33Rd sp Rk sp Rsp N N γ===N >N=5544 N混凝土劈裂破坏承载力满足规范要求! 4、锚栓钢材受剪破坏承载力锚栓钢材破坏时的受剪承载力标准值:,0.50.55850014500Rk s s stk V A f ==⨯⨯=N锚栓钢材受剪承载力分项系数:,5001.2/ 1.22.0300Rv s stkyk f f γ==⨯=锚栓钢材破坏时的受剪承载力设计值:,,,/14500/27250Rd s Rk s Rs v V V N γ===>V=2074 N锚栓钢材受剪承载力满足规范要求! 5、混凝土楔形体受剪破坏承载力取c 1=c 2=,90cr Nc=mm混凝土楔形体破坏时的受剪承载力标准值:,00.21.51/)Rk c f nom V l d =0.2 1.50.45(60/10)90==10285.86 N边距比c 2/c 1对受剪承载力的降低影响系数:2s,1900.70.30.70.30.91.5 1.590v c c ψ=+=+⨯=⨯边距与构件厚度比c 1/h 对受剪承载力的提高影响系数:1/31/31, 1.5 1.590()()0.814250h v c h ψ⨯===<1,取, 1.0h v ψ= 剪力与垂直于构件自由边方向轴线之夹角α对受剪承载力的影响系数,v αψ: 因为α=00,因此, 1.0v αψ=。
荷载偏心对群锚受剪承载力的降低影响系数,ec v ψ:ec,1110.62828012/31390v v e c ψ===⨯++⨯未开裂混凝土及锚固区配筋对受剪承载力的提高系数,ucr v ψ:, 1.0ucr v ψ=单根锚栓受剪,混凝土破坏楔形体在侧面的投影面面积:022,14.5 4.59036450c V A c ==⨯=mm2群锚受剪,混凝土破坏楔形体在侧面的投影面积:,122(1.5)(1.59020090)250106250c V A c s c h =++=⨯++⨯=mm 2群锚混凝土楔形体破坏时的受剪承载力标准值:,0,,,,,,0,c V Rk c Rk cs V h V ec V ucr V c VA V VAψψψψ=10625010258.860.9 1.0 1.00.628 1.036450=⨯⨯⨯⨯⨯⨯=16901.79 N混凝土楔形体受剪承载能力分项系数:Re, 1.8v γ=群锚混凝土楔形体破坏时的受剪承载力设计值:,,,/16901.79/1.89389Rd c Rk c Rc V V V γ===N >V=2074 N混凝土楔形体受剪承载力满足规范要求! 6、混凝土剪撬破坏承载能力因为903060mm ef h =-=≥60 mm ,故取K=2.0。
混凝土剪撬破坏承载能力标准值:R,, 2.017138.8434277.68k cp Rk c V kN ==⨯=N混凝土剪撬破坏承载能力分项系数:R 1.8cp γ=混凝土剪撬破坏承载能力设计值:R ,,/34277.68/1.819043.16d cp Rk cp Rcp V V γ===N >V=2074 N混凝土剪撬破坏承载力满足规范要求! 7、拉剪复合受力承载力植筋钢材破坏:2222,,22161037()()()()0.044145007250h h Sd Sd Rd s Rd s N V N V +=+=<1.0 混凝土破坏:1.5 1.5 1.5 1.5,,55442074()()()()0.5469548.819389.88h h Sd Sd Rd s Rd s N V N V +=+=<1.0 综上所述,后置埋件的承载力满足规范要求!>> As=58 f_stk=500N_RKs=As*f_stk f_yk=300gamma_RSN=(1.2*f_stk)/f_yk N_RdS=N_RKs/gamma_RSNh_ef=110h_ef1=h_ef-30f_cuk=35N_RKc0=(3.0*(h_ef-30)^1.5)*sqrt(f_cuk)S_crN=3*h_ef1C_crN=1.5*h_ef1C_crsp=2*h_ef1C=120psi_sN=0.7+(0.3*c)/C_crNpsi_reN=0.5+h_ef1/200e_N=0s_crN=180psi_ecN=1/(1+(2*e_N)/s_crN)psi_ucrN=1S_crN=150A_cN0=S_crN^2s_1=120s_2=120s_2=120c_1=120c_2=120A_cN=(c_1+s_1+0.5*S_crN)*(c_2+s_2+0.5*S_crN)gamma_RcN=2.15N_RKc=(N_RKc0*A_cN*psi_sN*psi_reN*psi_ecN*psi_ucrN)/A_cN0 N_Rdc=N_RKc/gamma_RcNc_crsp=2*h_ef1s_crsp=2*c_crsps_1=120s_2=120A_cN0=s_crsp^2A_cN=(c_1+s_1+0.5*s_crsp)*(c_2+s_2+0.5*s_crsp)h=500psi_hsp=(h/(2*h_ef))^(2/3)N_RKc0=(3.0*(h_ef-30)^1.5)*sqrt(f_cuk)N_RKc=(N_RKc0*A_cN*psi_sN*psi_reN*psi_ecN*psi_ucrN)/A_cN0 N_RKsp=psi_hsp*N_RKcgamma_Rsp=2.15N_Rdsp=N_RKsp/gamma_Rspgamma_Rsv=(1.2*f_stk)/f_ykV_Rds=N_RdS/gamma_Rsvc_1=C_crNc_2=C_crNl_f=90d_nom=12V_RKc0=0.45*sqrt(d_nom)*(90/60)^(0.2)*sqrt(f_cuk)*c_1^(1.5) psi_sv=0.7+(0.3*c_2)/(1.5*c_1)psi_hv=((1.5*c_1)/h)^(1/3)psi_alphav=1.0e_v=225psi_ecv=1/(1+(2*e_v)/(3*c_1))psi_ucrv=1A_cV0=4.5*(c_1^2)A_cV=(1.5*c_1+s_2+c_2)*hV_RKc=(V_RKc0*A_cV*psi_sv*psi_hv*psi_ecv*psi_ucrv)/A_cV0 gamma_Rev=1.8V_Rdc=V_RKc/gamma_Revh_ef=110K=2V_RKcp=K*N_RKcgamma_Rcp=1.8V_Rdcp=V_RKcp/gamma_RcpN_Sdh=444.83V_Sdh=4846beta=((N_Sdh/N_RdS)^2)+((V_Sdh/V_Rds)^2)beta_1=((N_Sdh/N_RdS)^(3/2))+((V_Sdh/V_Rds)^(3/2))As =58f_stk =500N_RKs =29000f_yk =300gamma_RSN =2N_RdS =14500 >N_ Sdh = 1.2376e+03 (锚栓钢材受拉破坏承载力)h_ef =110h_ef1 =80f_cuk =35N_RKc0 =1.2700e+04S_crN =C_crN =120C_crsp =160C =120psi_sN =0.9750psi_reN =0.9000e_N =s_crN =180psi_ecN =1psi_ucrN =1S_crN =150A_cN0 =22500s_1 =120s_2 =120s_2 =120c_1 =120c_2 =120A_cN =99225gamma_RcN =2.1500N_RKc =4.9145e+04N_Rdc =2.2858e+04 >N_ Sdh = 1.2376e+03 (混凝土锥体受拉破坏承载力)c_crsp =160s_crsp =s_1 =120s_2 =120A_cN0 =102400A_cN =160000h =500psi_hsp =1.7286N_RKc0 =1.2700e+04N_RKc =1.7412e+04N_RKsp =3.0099e+04gamma_Rsp =2.1500N_Rdsp =1.4000e+04 >N_ Sdh = 1.2376e+03 (混凝土劈裂破坏承载力)gamma_Rsv =2V_Rds =7250> V_sdh = 5.9934e+03 (锚栓钢材受剪破坏承载力)c_1 =120c_2 =120l_f =90d_nom =12V_RKc0 =1.3147e+04psi_sv =0.9000psi_hv =0.7114psi_alphav =1e_v =psi_ecv =0.4444psi_ucrv =1A_cV0 =64800A_cV =210000V_RKc =1.2124e+04gamma_Rev =1.8000V_Rdc =6.7353e+03> V_sdh = 5.9934e+03 (混凝土碶形体受剪破坏承载力)h_ef =110K =2V_RKcp =3.4825e+04> V_sdh = 5.9934e+03 (混凝土剪撬破坏承载力标准值)gamma_Rcp =1.8000V_Rdcp =1.9347e+04N_Sdh =444.8300V_Sdh =4846beta =0.4477<1 (拉剪复合承载力:植筋破坏)beta_1 =0.5518<1 (拉剪复合承载力:混凝土破坏)综上所述,后置埋件的承载力满足规范要求。